Cálculo de la cinta transportadora 2: auxiliar

Based on our assessment of the broader literature and the existing viability assessments and scientific results to date on Scandinavian wolves, we have synthesized science-based criteria to ensure that the wolf population in Scandinavia maintains status as a “Favorable Reference Population” (FRP). The criteria we describe are conceptually sound and directly relevant to Scandinavian wolves.

It seems clear that the persistence of wolves in Scandinavia, as elsewhere in the world, will depend on human tolerance. Wolves have a remarkable ability to increase numbers in the face of mortality, including that from controlled hunting. Thus, we do not see hunting per se as incompatible with FRP status. However, illegal hunting (poaching) can decimate or slow the restoration of any population, including Scandinavian wolves, where currently the population continues to increase even as half of total mortality comes from poaching (Liberg et al. 2012).

The criteria for FRP that we have suggested will surely not be easy to implement. However, we believe they are biologically defensible, and consistent with our review of the Scandinavian wolf literature and broader conservation biology concepts. In some cases they are more moderate than criteria that some others have proposed. We do not believe the level of social tolerance (e.g. social carrying capacity) should be confused with the biological thresholds for FRP, or that genetic or population health should be sacrificed for political expediency. However, we also acknowledge the stark reality that social tolerance – and its feedback effects on wolf survival and persistence -- will be promoted by good faith in setting biological criteria. We have certainly seen that reality in play in our experience with wolves in the western U.S., where moderate stakeholders became vehemently anti-wolf when they perceived the thresholds were being set for a political agenda instead of based on sound science. Of course, some of this is perception only (Räikkönen et al. 2013). Nevertheless, we believe that our moderate criteria for population sizes and connectivity, coupled with our advocacy for controlled hunting as part of FRP management, are both biologically defensible and less likely to initiate massive increases in mortality due to poaching that could very quickly and drastically undercut population persistence.

We do not find a defensible basis for using long-term, highly managed physical translocations of wolves to maintain connectivity. While we recognize that occasional human facilitated movements of wolves over short distances to bypass conflict zones may be necessary, we believe that for both biological and socio/political reasons managed translocations should not be implemented as a replacement for natural dispersal.

27 Finally, we realize that our proposal for a “two-tier” FRP status for Sweden (300 for population viability as part of a functional metapopulation, growing ultimately towards 600 for an ecologically viable population) may be problematic with respect to existing policies, laws, and guidelines. We favor this approach because we believe enacting FRP status at current (biologically justified) population sizes and metapopulation dynamics, and allowing controlled harvest, will simultaneously foster continued growth in the wolf population towards a size closer to ecological viability (with higher public acceptance). We believe the approach is technically possible in this case, because of the remarkable detail and rigor of the Scandinavian wolf monitoring program. The work of the SKANDULV team gives a luxury unavailable for most species around the world: to manage adaptively with a strong scientific evidence-based framework. This adaptive monitoring framework allows us to propose that wolves in Sweden can be

considered to be at FRP currently, and that FRP status would continue as long as the monitoring program supports progress towards a long-term goal of 600 wolves.

28 APPENDIX I: Calculating Scandinavian Wolf Growth Rate in a Stochastic Environment

The most commonly used models to estimate exponential trend assume that only one form of variation -- either sampling or process variance -- is present in the time series data. For example, one widely used method of estimating trend from a time series of abundance values uses a simple linear regression of natural log (ln) of abundances (N) against time (the natural log accounts for the fact that birth and death processes cause populations to change

geometrically, not arithmetically). The slope of the regression of ln(N) vs time represents the estimated average rate of change (ˆr =ˆ), which converts to λ, the discrete stochastic geometric growth rate, as ˆr =ˆ = ln(λ). The simplicity of the method explains its popularity, but the method has a major limitation: it assumes that all variation in the trend arises only from the uncertainty in estimating abundance (i.e., pure observation error or sample variance; Humbert et al. 2009). That is, this method assumes that population growth is completely constant -- unaffected by process variance arising from weather, predators, or other environmental conditions -- so that all deviations in abundances from the trend line arise solely from the uncertainty of estimating abundances.

A suite of other widely used methods make the opposite assumption, that no observation error exists and that all variation in the trend arises from process variance or process noise (e.g., the diffusion approximation; Dennis et al. 1991). When the time series is complete (with no missing years), one form of this “Process Noise Only” model is to estimate the geometric mean of multiple consecutive measurements of λ over time (Humbert et al. 2009 ; Mills 2013).

Although it does not have a big effect in this case, the SKADULV reports erroneously estimate average growth rate from the arithmetic mean of the consecutive λ values in the wolf time series. Because population growth is a geometric, not arithmetic process, the most likely growth rate is characterized by the geometric mean, not the arithmetic mean. In fact, as stochasticity increases, the arithmetic mean of consecutive will increasingly overestimate the most likely λ (Case 2000, Mills 2013). As a very simple example (that would not be impossible for a wolf population) consider 3 years where the abundance of a population size went from 100 to 150 and back to 100. The two λ consecutive values would be 1.5 and 0.67. The arithmetic mean of these two lambda values would be 1.08 (implying an 8% increase per year, on average), but the (correct) geometric mean lambda would be 1.0 (stationary population).

We emphasize that this error does not affect in any meaningful way the SKADULV reports to date. For example, if we compare the arithmetic mean lambda to the geometric mean lambda in

the SKADULV 1998-2014 time series (Sand et al. 2014), the difference is only at the 2nd decimal place (λ= 1.13 for arithmetic mean vs 1.12 for geometric mean). Nevertheless, the distinction is important because the error will increase with greater variation in numbers.

In any case, determining the most likely trend λ from the geometric mean of the consecutive λ values is, as mentioned above, a Process Noise Only estimator that does not account for any sampling uncertainty in the estimation of N from year to year.

29 In contrast, the state space model we use in the main text estimates stochastic

exponential population growth (the average instantaneous per capita growth rate) as [ r ] =ˆ ₌ Ln(λ)) (Humbert et al. 2009; see accessible overview in Mills 2013 Chapter 5). In addition to a confidence interval that incorporates both sample (observation) variance (denoted by _ˆ2

) and process variance due to environmental and demographic stochasticity (denoted _ˆ2_{), the model}

also provides separate estimate of _ˆ2

and _ˆ2

.

We have found through simulations (Humbert et al. 2009) that the estimates of mean trend will not differ much among the different estimators but the confidence intervals can be quite different, so that the CI from one estimator may overlap 1 and imply no increase while another does not, implying an increasing population.

Therefore, we recommend use of the state space estimator, because it more realistically accounts for both process and sample variance. (Other state space models are available and have been used for Scandinavian wolves: e.g. Chapron 2012, Sand, Liberg and Chapron 2014).

Applying the Humbert et al. 2009 state space model to the SKADULV Scandinavian wolf data from 1998-2014 gives an estimate of ˆ _{= 0.120, with a 95% confidence interval of} (0.105 to 0.135). Converting these to λ, gives λ=1.13 (by coincidence, this is the same value as the erroneous arithmetic mean of the values, but nothing should be made of that) with 95% confidence limits of λ from 1.11 to 1.14 . Updating the time series to include the most recent 2014/15 abundance estimate, gives an estimate of ˆ _{= 0.120, with a 95% confidence interval of} (0.107 to 0.132). Converting the estimate of ˆto λ, gives λ = 1.12 with 95%CI of λ: 1.11 – 1.14. This growth rate represents a 13% increase in the population size each year, on average. Because the confidence intervals do not overlap a stationary population [ˆ= 0 or (λ=1)], the positive growth rate can be considered statistically significant.

In summary, we concur with the widespread view that the Scandinavian wolf

population is strongly increasing; the 95% confidence interval of trend is well above a stationary trajectory. For future use, we encourage the use of the state space estimator to describe most likely stochastic growth rate and its confidence interval. Finally, if the wolf team feels that it is necessary to use the Process Noise Only model to estimate population trend over time, we encourage the use of the geometric mean, not the arithmetic mean lambda.

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